Cross-Error Correcting Integer Codes over ℤ2m

In this work we investigate codes in Zⁿ_2m that can correct errors that occur in just one coordinate of the codeword, with a magnitude of up to a given parameter t. We will show upper bounds on these cross codes, derive constructions for linear codes and respective decoding algorithm. The constructions (and decoding algorithms) are given for length n = 2 and n = 3, but for general m and t.